Quantum Harmonic Oscillator

Time-dependent Schrödinger equation — coherent state dynamics
Coherent state |α⟩ = Gaussian
wave packet displaced by x₀.

Re(ψ) in blue, |ψ|² in green
V(x) = ½x² in orange

E_n = ℏω(n + ½)

Coherent states oscillate
without spreading — the most
"classical" quantum states.